Two uniform smooth spheres \(A\) and \(B\), of equal radii, have masses \(m\) and \(2m\) respectively. The two spheres are moving with equal speeds \(u\) on a smooth horizontal surface when they collide.

Immediately before the collision, \(A\)'s direction of motion makes an angle of \(60^\circ\) with the line of centres, and \(B\)'s direction of motion makes an angle \(\theta\) with the line of centres. The coefficient of restitution between the spheres is \(e\).

After the collision, the component of the velocity of \(A\) along the line of centres is \(v\), and \(B\) moves perpendicular to the line of centres. Sphere \(A\) now has twice as much kinetic energy as sphere \(B\).

(a) Show that \(v=\dfrac12u(4\cos\theta-1)\).

(b) Find the value of \(\cos\theta\).

(c) Find the value of \(e\).